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Hard problem on partial differentiation

jaychay

Member
Sep 1, 2020
56
Untitled 4.png

Can you please help me ?
I have tried to do it many times but I end up getting the wrong answer.
Thank you in advance.
 

jaychay

Member
Sep 1, 2020
56
I finally got the answer to the question.


Untitled 5.png
 

skeeter

Well-known member
MHB Math Helper
Mar 1, 2012
1,017
$\dfrac{d}{dx}[f(x)h(x)] = f’(x)h(x) + f(x)h’(x)$

$\displaystyle f(x)h(x) = \int f’(x)h(x) \, dx + \int f(x)h’(x) \, dx$

$\displaystyle (x+1)^5 = \sin{x} + \int f(x)h’(x) \, dx$

finish it ...
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
881
I think this is a problem on "integration by parts", NOT "partial differentiation".